Obtain a Lotka-Volterra model with a recuring limit?

Struggling to code a Lotka-Volterra model , I keep getting the recursion exceeded error message.

LVmodel.nb (86.6 KB)

I would avoid using subscripts in function names. Try replacing Subscript[U, 1], Subscript[U, 2] with u1,u2.

Thanks, will try this.